Reny Kunnel Chacko George , Prof
• 5888140
• 0550426471

## Profile

PERSONAL INFORMATION

Name                                   :         RENY GEORGE

Date of Birth (DD/MM/YY)    :                  02/07/1963                 Age: 54 Years      Sex : Male

Permanent Address             :        C-21, Anandapuram Phase II, Junwani-Kohka Road

Bhilai,  Chhattisgarh State, India  Pin Code : 490006

Mobile : 00919630912469, 918827813037,  00919893520065

Present Address                     :           Department of Mathematics, College of Science

Prince Sattam bin Abdulaziz University

Al Kharj, Kingdom of Saudi Arabia

Mobile : 00966550426471

Email                                :               renygeorge02@yahoo.com

Place of Birth :  Dalli  Rajhara                                                 Nationality:   Indian

Marital Status: Married                                                 Number of Children:  02

## Education

 Particulars Discipline/Subject/Specialisation Name of School/College/University Year of Passing Passing of Marks\Division\along with Percentage Inter/ 2 English Hindi Physics Chemistry Mathematics B.S.P Higher Secondary School No.1, Dalli Rajhara (Board of Secondary Education, Bhopal) 1980 I Division, 64.3% Graduation B.Sc Pure Mathematics Applied Mathematics Physics St. Alloysius College Jabalpur/Rani Durgavati University, Jabalpur, India 1983 II Division, 56.1% Post Graduation M.Sc (Mathematics) Specialisation : Algebra, Analysis and Topology University Teaching Department, Rani Durgavati University, Jabalpur, India 1985 I Division, 77.75% Doctoral Ph D in Mathematics (Functional Analysis) Pt. Ravishankar Shukla University, Raipur, India 1996

## Achievements

Some of the major scientific contribution of  Prof Reny George are listed as follows:

·  Framed  weaker  form  of  non-commutative  mappings   such  as compatible mappings of type (A1) and type (A2),  coincidentally commuting mappings (later renamed as occasionally weak compatible mappings), co-ordinatewise compatible mappings and Horizontally weakly compatible mappings. These results were found viable, productive and applicable to solve problems of existence and uniqueness of solutions of certain nonlinear integral equations, functional equations arising in dynamic programming problems, best approximation problem, variational inequalities arising in two   point   obstacle  problems  in stochastic game theory etc.

· Introduced the new class of Dislocated Fuzzy Metric Space and successfully extended the Banach Contraction Principle and Jungck Contraction Principle to this space.

· Proved the existence   of   common   fixed  point  for  a  Banach   operator  pair    under  certain  generalized  contractions to obtain some best  approximation  results and  applied  these results for the first time to the problem of existence of  solutions of  variational inequalities  and the solution of functional equations arising from  dynamic  programming.

· In the year 2015 introduced the new class of Rectangular b-Metric Space as a generalization of metric space, b-metric space and rectangular metric space and studied their topological properties. The  Banach Contraction Principle and Kannan Contraction Principle were extended to this space.  The class of  Rectangular b-Metric Space has now become an important tool in metric fixed point theory with many researchers successfully extending and generalizing many fixed point results in this space and finding applications of these results in integral equations, functional equations , variational inequalities etc.

·   Solved   new problems of existence of solution of a pair of simultaneous variational inequalities and also a pair of simultaneous complimentarity problems  via fixed points.

· Introduced the new class of Generalised Cone b-Metric Space as a generalization of metric space, b-metric space , cone b-metric space and rectangular metric space and studied their topological properties. The  Banach Contraction Principle and  Kannan Contraction Principle were extended to such spaces.

·  Framed Presic contraction and Jungck-Presic contraction for the first time in a cone metric space and established the existence of common fixed points for such contraction mappings in cone metric space. Applied the result in the problem of  finding a stationary distribution  of a Markov Process associated with the random process in which one of the n states is realised in each period t = 1,2,… with the probability conditioned on the current realised state.

· Framed Presic-Hardy Rogers contraction and Ciric-Presic contraction for two mappings in a b-metric space and established the existence of common fixed points of such contraction pair of mappings in b-metric space. Applied this result in deriving some convergence result for a system of matrix equations and also provided numerical experiments to illustrate the convergence algorithms.

· Introduced the new class of Rectangular Cone b_Metric Space over a Banach Algebra which contains metric space, b-metric space, cone metric space, cone b-metric space and rectangular b-metric space as subclass. Proved Banach contraction principle and weak Kannan contraction principle in such a space and applied the results in analyzing certain conditions to ensure the existence of solution of a system of linear equations.

·  Defined Proximal contractions of type I and type II in b-metric space and proved the existence of a best proximity point for such contraction mappings thereby ascertaining an optimal approximate solution to the equation Tx = x in a b-metric space.

·  Introduced the new class of Partial Rectangular b-metric space and gave its topological properties. Defined Wardowski-Ciric-Presic contraction mapping in a Partal Rectangular b-metric space and proved the existence of fixed point of such contraction mapping.

· Defined weak semi alpha admissibility, condition (G) and condition (G’) for a self mapping and used it for proving existence of unique fixed point of Perov type alpha-quasi contraction map, alpha-Kannan contraction map and alpha-Chatterjee contraction map defined in the newly introduced  dislocated cone metric space over Banach algebra.

## Experiences

1. WORK EXPERIENCE RELATED INFORMATION

Total experience: 32 Years:

Details of  experience :
i) Teaching                    : 32 Years

For the past 32  years, I have been delivering lectures in various courses of Mathematics to the students of Graduate and Post Graduate Programs.  The details of courses taught are as follows:

1. Under Graduate Level (B.Sc, B.E and B.C.A) : Calculus (Differential, Integral and Advanced), Differential Equations (Ordinary and Partial), Discrete Mathematics, Linear Algebra, Abstract Algebra(Group theory, Rings and Fields), Real Analysis, Complex Analysis, Mathematical Methods and Numerical Analysis.
2. Post Graduate Level (M.Sc): Topology, Real Analysis, Functional Analysis, Advanced Abstract Algebra, Complex Analysis and Operations Research.

College Level       : 10 Years  (As Principal/Dean)

Served as Principal (Dean) of St. Thomas college Bhilai in India. The college is a multidisciplinary institution with Arts, Science and Commerce faculties offering both Bachelor and Master degree programs, affiliated to Pt. Ravishankar Shukla University Raipur, India  and has around 85 teaching staff and 22 non teaching staff on its roll. Apart from teaching and research the duties included coordination with university authorities with regard to academic affairs, monitoring of academic activities in the college, supervising the duties of employees and writing their annual confidential reports, conduct of university examinations in the college, communicating with the management regarding budgetary requirements and expenditures, monitoring the staff requirement and initiating the recruitment process whenever required, liasoning with Government departments for procurement of funds  etc.

Department Level          : 17 Years (As Head of Department)

Worked as Head of Department of Mathematics and Computer Science at St. Thomas College, India and Eritrea Institute of Technology Eritrea. The duties included teaching in Graduate and Post Graduate level programs, allocating courses to faculty members of the department, monitoring the work of faculty members of the department and recommending for their promotions as and when they become eligible, recommending the university for any modifications in course curriculum as and when required, recommending the Head of the Institution for introduction of new programs in the department as per demand etc. Eritrea Institute of Technology (EIT) is a deemed university and as Head of The Department at EIT, apart from duties mentioned above I chaired the committee for curriculum designing and study material preparation for pre graduate and graduate programs.

Accreditation  Experience              :

National Level  : Worked as member of Peer Review Team of National Assessment and Accreditation Council (NAAC) of India. Visited four colleges as a team member for peer review of the institutional SSR for accreditation.

College Level :  Member of  Internal Quality Assurance Cell for four years at St. Thomas College, Bhilai, India. Chaired the college accreditation committee and  Internal Quality Assurance Cell for seven years at St. Thomas College, Bhilai, India. Member of college level accreditation committee and department level accreditation committee at Salman bin Abdulaziz University, Kingdom of Saudi Arabia.

Foreign assignments/visits :

·  Currently working as Professor of Mathematics at College of Science, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia.

·  Worked as Associate Professor and Head, in the Department of Mathematics, Eritrea Institute of Technology, Asmara, Eritrea, North East Africa from 5th November 2003  to 5th December 2005.

· Worked  as Associate Professor of Mathematics at Salman Bin Abdulaziz  University, Saudi Arabia from 5th November 2010 to 9th June 2013..

·  A short visit to Dukes University U.S.A, to deliver a talk in the Joint Conference on Information Sciences from 21st July to 26th July 2005.

·  A short visit to Sultan Quaboos University, Muscat, Sultanate of Oman, to deliver a talk in the International Conference in Analysis and Applications from 24th January to 26th January 2010.

·  A short visit to City University New York, 15th December 2013 .

## Research

SCIENTIFIC RESEARCH RELATED INFORMATION :

Field : Non Linear Analysis

Specialization : Fixed Point Theory and Applications, Generalized Metric Topologies,  Fuzzy sets and Theory.

1. Research Statistics
1. Google Scholar   (Total Citations : 144     h-Index : 7           i10-Index  : 5)
2. Research Gate    (Total Citations : 106       Total Reads : 1632   RG Score : 13.89 )

1. Researcher Id  : H-3325-2016

c)  Research Publications in International Peer Reviewed Journals.

 S. No Title Cooperated Author (s) Journal ( Volume, Issue, Date ) 1 Approximation of common fixed point of alpha-generalised contraction mappings in dislocated cone b-metric space over Banach Algebra and its applications Reny George, S. Radenovic , Hossam A Nabwey , R. Rajagopalan and S. Vinayakam Submitted in ISI Journal. 2 On Reich contraction principle in rectangular  b-metric space Reny George and Zoran D. Mitrović Submitted in ISI Journal. 3 Dislocated Cone Metric Space over Banach Algebra and  alpha-Quasi Contraction Mappings of Perov Type Reny George, R. Rajagopalan, Hossam A Nabwey and S. Radenovic Fixed Point Theory and Applications, Springer Open, 2017:24,  DOI 10.1186/s13663-017-0619-7 4 On Reich contraction principle in rectangular cone b-metric space over Banach algebra Reny George and Zoran D. Mitrović Journal of Advanced Mathematical Studies, 11(1), 2018, 10-16. 5 Rectangular cone b-metric space over Banach algebra and contraction principles. Reny George, Hossam A Nabwey, R. Rajagopalan, S. Radenovic and K.P Reshma Fixed Point Theory and Applications, Springer Open, 2017:14 , DOI 10.1186/s13663-017-0608-x 6 Cyclic contractions and fixed points via C-class functions in b-metric space and its application Reny George, M.S Khan, A.H Ansari and S. Vinayakam Accepted in Applied Mathematical Sciences (Hikari), Bulgaria. 7 Fixed Points of Wardowski- Ciric-Presic Type Contractive Mappings in a Partial Rectangular b-Metric Space Vahid Parvaney, Farhan Golkarmanesh and Reny George Journal of Mathematical Analysis, 8(1), 2017, 183-201. 8 Rectangular b-metric spaces and contraction principles Reny George, S.Radenovic, K.P Reshma and S.Shukla Journal of Non linear Science and Applications, 8(2015), 1005-1013. 9 Some generalized fixed point results in b-metric spaces and application to matrix equations H.K Pathak, Reny George, Hossam A Nabwey, Mahdy S El-Paoumy and K.P Reshma Fixed Point Theory and Applications, Springer Open, 2015, DOI:10.1186/s13663-015-0343-0 11 Generalised cone b-metric spaces and contraction principles Reny George, Hossam E Nabwey, R.Rajagopalan and K.P Reshma Matematicki Vesnik, Vol. 67, No. 4, pp. 246-257 (2015). 11 Fixed point theorems for cyclic contractions in b-metric spaces Reny George, K.P Reshma and Padmavathi Journal of Nonlinear Functional Analysis, SCIK Publishing Corporation, U.K , 2015:5 12 On best proximity points in b-metric space Reny George, Cihangir Alaca and K.P Reshma Journal of Nonlinear Analysis and Applications, 2015(1), 45-56. Doi : 10.5899/2015/jnaaq-00278. 13 Horizontally weak compatibility of mappings and fixed points in a dislocated fuzzy metric space Reny George, Hossam E Nabwey, K.P Reshma and R.Rajagopalan Applied  Mathematical Sciences, Hikari Ltd, (Ruse), Bulgaria, 2014, 8(113), 5641-5652 14 Common fixed point theorems for single and set valued horizontally weakly compatible pairs of mappings in dislocated fuzzy metric spaces R.Rajagopalan , Reny George, M.S Khan and  K.P Reshma International Journal of Mathematical Analysis, Hikari Ltd, (Ruse), Bulgaria, 2014, 8(14), 683-697. 15 Some fixed point results of Presic type in b-metric spaces Reny George Mathematical Sciences International Research Journal, India, 2(2), 2013 16 Some generalized results of fixed points in cone b-metric spaces Reny George and Brian Fisher Mathematica Moravica, Serbia,17(2), 2013 17 Common fixed point results for $\psi$ - $\phi$ contractions in  Rectangular Metric Spaces Reny George and             R. Rajagopalan Bulletin of Mathematical Analysis and Applications, Kosova, 5(1), 2013. 18 Presic type hybrid contractions and fixed points in cone metric spaces Reny George Advances in Fixed Point Theory, SCIK Publishing Corporation, U.K, 3(1),2013. 19 Cyclic contractions and fixed points in Dislocated Metric Spaces Reny George, R. Rajagopalan and S. Vinayagam International Journal of Mathematical Analysis, Hikari Ltd, (Ruse), Bulgaria,  Vol 7(9), 2013. 20 Dislocated fuzzy quasi metric spaces and fixed points Reny George and S.M Kang Annals of Fuzzy Mathematics and Informatics, Kyung Moon Sa, Korea. Vol 5, Issue 1, 2013. 21 Some fixed point results in dislocated fuzzy metric spaces Reny George Journal of Advanced Studies in Topology, Modern Science Publishers, Egypt, Vol 3, Issue 4), 2012. 22 On dislocated fuzzy topologies and fixed points Reny George and R.A Rashwan Journal of Mathematics Research, CCSE, Canada, Vol 4(1), 2012 23 A generalized fixed point theorem of  Presic type in cone metric space and application to Markov process Reny George, K.P Reshma and R. Rajagopalan Fixed Point Theory and Applications , Springer Open, 2011, 2011:85 24 Presic type extension and generalization of Banach Contraction Principle Reny George and M.S Khan International Journal of Mathematical Analysis, Hikari Ltd, Ruse 5(21),2011, 1019-24. 25 Variational inequalities and their solutions via fixed points Reny George, M.S Khan and K.P Reshma Advances in Nonlinear Variational Inequalities, International Publishers, USA, Vol 12, Issue 1, 2009. 26 On commutativity and its generalizations in hybrid fixed point theory Reny George, M.S Khan and H.K Pathak Non linear Functional Analysis and Applications, Kyungnam University Press, Korea, Vol 13, Issue 1, 2008 27 Compatible mappings of type(A-1) and type (A-2) and common fixed points in Fuzzy metric spaces M.S Khan, H.K Pathak and Reny George International Mathematical Forum, Hikari Ltd, Ruse, Vol 2, Issue 11, 2007. 28 Fixed point theorems for hybrid mappings in metric spaces Reny George, M.S Khan and Abraham Varghese Mathematica Moravica, University of Kragujevac, Vol. 10, 2006. 29 Dislocated fuzzy metric spaces and associated topologies. Reny George and M.S Khan Proceedings of Joint Conference on Information Sciences, Track- 10th International Conference on Fuzzy Theory and Technology, Salt Lake City, USA, 21st July to 26th July 2005. 30 Coincidence and common fixed points of non self hybrid mappings in metrically convex spaces H.K Pathak, Reny George and M.S Khan Non linear Functional Analysis and Aplications, Kyungnam University Press, Korea, Vol 10, Issue 2, 2005 31 Simultaneous Complimentarity problems and their solutions via fixed points. H.K Pathak, Reny George, S.M Kang and Y.J Cho Pure Mathematics and Applications, Hungary, Vol 7, Issue 1-2, 1995 32 A common fixed point theorem of Gregus type for compatible mappings and its applications. H.K Pathak and Reny George Publications Mathematicae, Hungary, Vol 44, Issue 3-4, 1994

Research Papers in International Seminars and Conferences :

 S.No Seminars/Conference Duration Description 1 INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLICATIONS – 2010, SULTAN QUABOOS UNIVERSITY, MUSCAT, SULTANATE OF OMAN 24TH JANUARY TO 26TH JANUARY 2010 Delivered a Talk titled “Presic type   extension and generalization of Banach contraction principle” 2 JOINT CONFERENCE ON INFORMATION SCIENCES, TRACK - 10TH   INTERNATIONAL     CONFERENCE ON FUZZY THEORY AND  TECHNOLOGY,  SALT LAKE CITY, U.S.A 21ST JULY TO 26TH JULY 2005 Delivered a Talk titled  “Dislocated fuzzy metric spaces and associated  topologies” 3 ANNUAL CONFERENCE OF BANARAS MATHEMATICAL SOCIETY  HELD AT BANARAS HINDU UNIVERSITY, BANARAS, U.P  INDIA 1993 Presented a paper 4 ANNUAL CONFERENCE OF INDIAN MATHEMATICAL  SOCIETY  HELD AT D.V POST  GRADUATE COLLEGE , ORAI ,U.P  INDIA 1996 Presented a paper 5 NATIONAL CONFERENCE ON “ RECENT TRENDS IN ANALYSIS WITH EMPHASIS ON  HISTORY OF MATHEMATICS” HELD AT PT. RAVISHANKAR SHUKLA   UNIVERSITY  RAIPUR. INDIA 2003 Presented a paper

d) Supervision of  Research:

 Research Title Institution Completed/Ongoing Master/Ph.D. Studies on certain aspects of fixed point theorems  in different topological spaces and their applications Pt. Ravishankar Shukla University, Raipur, India Completed 2016 Ph D Studies on fixed point theorems of certain class of  single valued as well as  multi valued mappings in different topological spaces and their applications Singhania University, Jhunjunu, Rajasthan, India Completed 2014 Ph D

e) Reviewer for Research Journals:  Reviewing research articles for the following mathematical journals :

1. American Mathematical Society, Mathematical Reviews, U.S.A
2. Fixed Point Theory and Applications (Springer Open).
3. Matematicki Vesnik, Serbia
4. Journal of Non-linear Sciences and Applications, Iran.
5. Fixed Point Theory (Romania).
6. Revista de la Real Academia de Ciencas Exactas, Fisicas y Naturales. Serie A. Matematicas, Romania
7. Facta Universitatis , Series : Mathematics and Informatics, Serbia.
8. Annals of Fuzzy Mathematics and Informatics, Korea.
9. Journal of Advanced Studies in Topology, Egypt.
10. Bulletin of Malaysian Mathematical Society.
11. Annals of Alexandru Loan Cuza University-Mathematics
12. Bulletin of Calcutta Mathematical Society, India
13. Indian Journal of Mathematics
14. Journal of Scientific Research and Reports, SCIENCEDOMAIN International
15. Non Linear Analysis : Modelling and Control
16. Filomat, Serbia.

f) Research Collaborations :  Collaborated with many researchers from different part of the world. Some of them are as follows:

1. Prof Brian  Fisher, University of Liecester, U.K.
2. Prof Stojan Radenovic, University of Belgrade, Serbia.
3. Prof Mohammad Saeed Khan, Sulthan Quaboos University, Oman.
4. Prof Y.J Cho, Gyeongsang National University, S.Korea.
5. Prof H.K Pathak, Ravishankar Shukla University, India.
6. Prof S.M Kang, Gyeongsang National University, S.Korea.
7. Prof Cihangir Alaca,  Celal Bayar University, Turkey.
8. Dr. Vahid Parvaneh, Islamic Azad University, Iran.
9. Dr. Satish Shukla, V.D College of Engineering, Indore, India.
10. Dr. Zoran D Mitrovic, University of Banja Luka, Bosnia and Herzegovina.

g) Research Projects

 Title Funding Agency Status Applications of Fixed Point Theorems University Grants Commission, India Grant No. 4-126(8)/98(MRP/CRO) Completed Fixed Point Theorems in Cone and Fuzzy Metric Spaces and their Applications Deanship of Scientific Research, Prince Salman bin Abdulaziz University, Al-Kharj, Kingdom of Saudi Arabia. Grant No. 1433/T/36. Completed A comprehensive study of certain fixed point results  and their applications with special emphasis on variational inequalities and matrix equations Deanship of Scientific Research, Prince Salman bin Abdulaziz University, Al-Kharj, Kingdom of Saudi Arabia. Grant No. 2014/01/2046. Completed Studies on Generalised Metric Fixed Point Theory and Applications. Deanship of Scientific Research, Prince Sattam  bin Abdulaziz University, Al-Kharj, Kingdom of Saudi Arabia. Grant No. 2016/01/671 Ongoing

## Citations

1. Research Statistics
1. Google Scholar   (Total Citations : 144     h-Index : 7           i10-Index  : 5)
2. Research Gate    (Total Citations : 106       Total Reads : 1632   RG Score : 13.89 )

1. Researcher Id  : H-3325-2016