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Applicable Analysis
An International Journal
Volume 22, 1986 - Issue 3-4
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Original Articles

A note on the solution of a class of functional equations

R. Baskaran Department of Mathematics, Indian Institute of Technology, Madras, India
&
P.V. Subrahmanyam Department of Mathematics, Indian Institute of Technology, Madras, India
Pages 235-241 | Received 18 Oct 1985, Published online: 02 May 2007

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Zeqing Liu, Liangshi Zhao, Shin Min Kang & Jeong Sheok Ume. (2011) On the solvability of a functional equation. Optimization 60:3, pages 365-375.
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Mujahid Abbas, Rizwan Anjum & Vasile Berinde. (2021) Enriched Multivalued Contractions with Applications to Differential Inclusions and Dynamic Programming. Symmetry 13:8, pages 1350.
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Naeem Saleem, Mujahid Abbas & Zahid Raza. (2020) Fixed fuzzy point results of generalized Suzuki type F-contraction mappings in ordered metric spaces. Georgian Mathematical Journal 27:2, pages 307-320.
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Anju Panwar & Anita. (2018) Metric-like space and Suzuki type common fixed point results with (W.C.C) condition. Asian-European Journal of Mathematics 13:03, pages 2050066.
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SHARMA PRANJALI & DHAR DIWAN SHAILESH. (2020) COMMON FIXED POINT RESULTS IN FUZZY METRIC SPACES WITH APPLICATIONS IN DYNAMIC PROGRAMMING. i-manager’s Journal on Mathematics 9:1, pages 38.
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Eskandar Ameer, Muhammad Arshad & Nawab Hussain. (2019) On new common fixed points of multivalued $$(\varUpsilon ,\varLambda )$$-contractions in complete b-metric spaces and related application. Mathematical Sciences 13:4, pages 307-316.
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Eskandar Ameer, Muhammad Arshad, Dong Shin & Sungsik Yun. (2019) Common Fixed Point Theorems of Generalized Multivalued (ψ,ϕ)-Contractions in Complete Metric Spaces with Application. Mathematics 7:2, pages 194.
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Eskandar Ameer, Hassen Aydi, Muhammad Arshad, Habes Alsamir & Mohd Noorani. (2019) Hybrid Multivalued Type Contraction Mappings in αK-Complete Partial b-Metric Spaces and Applications. Symmetry 11:1, pages 86.
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Erdal Karapınar, Kenan Taş & Vladimir Rakočević. 2019. Mathematical Methods in Engineering. Mathematical Methods in Engineering 3 66 .
Aftab Hussain, Muhammad Arshad & Mujahid Abbas. (2017) NEW TYPE OF FIXED POINT RESULT OF FCONTRACTION WITH APPLICATIONS. Journal of Applied Analysis & Computation 7:3, pages 1112-1126.
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Stojan RADENOVIĆ, Peyman SALIMI, Calogero VETRO & Tatjana DOŠENOVIĆ. (2016) Edelstein-suzuki-type results for self-mappings in various abstract spaces with application to functional equations. Acta Mathematica Scientia 36:1, pages 94-110.
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Mujahid Abbas, Basit Ali & Asma Rashid Butt. (2014) Existence and data dependence of the fixed points of generalized contraction mappings with applications. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 109:2, pages 603-621.
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Hassen Aydi, Manel Jellali & Erdal Karapınar. (2014) Common fixed points for generalized $$\alpha $$ α -implicit contractions in partial metric spaces: consequences and application. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 109:2, pages 367-384.
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Calogero Vetro, Sunny Chauhan, Erdal Karapınar & Wasfi Shatanawi. (2014) Fixed Points of Weakly Compatible Mappings Satisfying Generalized $$\varphi $$ φ -Weak Contractions. Bulletin of the Malaysian Mathematical Sciences Society 38:3, pages 1085-1105.
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Naeem Saleem, Basit Ali, Mujahid Abbas & Zahid Raza. (2015) Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications. Fixed Point Theory and Applications 2015:1.
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Sunny Chauhan, Stojan Radenović, Mohammad Imdad & Calogero Vetro. (2013) Some integral type fixed point theorems in Non-Archimedean Menger PM-Spaces with common property (E.A) and application of functional equations in dynamic programming. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 108:2, pages 795-810.
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Hassen Aydi, Mujahid Abbas & Calogero Vetro. (2013) Common fixed points for multivalued generalized contractions on partial metric spaces. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 108:2, pages 483-501.
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Sunny Chauhan, Hassen Aydi, Wasfi Shatanawi & Calogero Vetro. (2013) Some Integral Type Fixed-Point Theorems and an Application to Systems of Functional Equations. Vietnam Journal of Mathematics 42:1, pages 17-37.
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Abdul Rahim Khan, Mujahid Abbas, Talat Nazir & Cristiana Ionescu. (2014) Fixed Points of Multivalued Contractive Mappings in Partial Metric Spaces. Abstract and Applied Analysis 2014, pages 1-9.
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Basit Ali & M Abbas. (2013) Suzuki-type fixed point theorem for fuzzy mappings in ordered metric spaces. Fixed Point Theory and Applications 2013:1.
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Saurabh Manro, Satwinder Singh Bhatia, Sanjay Kumar & Calogero Vetro. (2013) A common fixed point theorem for two weakly compatible pairs in G-metric spaces using the property E.A. Fixed Point Theory and Applications 2013:1.
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M Abbas & Basit Ali. (2013) Fixed point of Suzuki-Zamfirescu hybrid contractions in partial metric spaces via partial Hausdorff metric. Fixed Point Theory and Applications 2013:1.
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Mujahid Abbas, Basit Ali & Calogero Vetro. (2013) A Suzuki type fixed point theorem for a generalized multivalued mapping on partial Hausdorff metric spaces. Topology and its Applications 160:3, pages 553-563.
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Ljubomir Ćirić, Mujahid Abbas, Miloje Rajović & Basit Ali. (2012) Suzuki type fixed point theorems for generalized multi-valued mappings on a set endowed with two b-metrics. Applied Mathematics and Computation 219:4, pages 1712-1723.
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Shyam Lal Singh, Swami Nath Mishra, Renu Chugh & Raj Kamal. (2012) General Common Fixed Point Theorems and Applications. Journal of Applied Mathematics 2012, pages 1-14.
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SL Singh, HK Pathak & SN Mishra. (2010) On a Suzuki Type General Fixed Point Theorem with Applications. Fixed Point Theory and Applications 2010:1.
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Zeqing Liu, Jeong Sheok Ume & Shin Min Kang. (2010) SOME EXISTENCE THEOREMS FOR FUNCTIONAL EQUATIONS AND SYSTEM OF FUNCTIONAL EQUATIONS ARISING IN DYNAMIC PROGRAMMING. Taiwanese Journal of Mathematics 14:4.
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SL Singh & SN Mishra. (2010) Remarks on Recent Fixed Point Theorems. Fixed Point Theory and Applications 2010:1, pages 452905.
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SL Singh & SN Mishra. (2009) Coincidence Theorems for Certain Classes of Hybrid Contractions. Fixed Point Theory and Applications 2010:1.
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Zeqing Liu, Lili Wang, Hyeong-Kug Kim & Shin-Min Kang. (2008) COMMON FIXED POINT THEOREMS FOR CONTRACTIVE TYPE MAPPINGS AND THEIR APPLICATIONS IN DYNAMIC PROGRAMMING. Bulletin of the Korean Mathematical Society 45:3, pages 573-585.
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Ke-Qing Wu, Nan-Jing Huang & Jen-Chih Yao. (2007) Existence Theorems of Solutions for a System of Nonlinear Inclusions with an Application. Journal of Inequalities and Applications 2007, pages 1-13.
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ZEQING LIU, JEONG SHEOK UME & SHIN MIN KANG. (2006) SOME EXISTENCE THEOREMS FOR FUNCTIONAL EQUATIONS ARISING IN DYNAMIC PROGRAMMING. Journal of the Korean Mathematical Society 43:1, pages 11-28.
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IN-SOOK KIM. (2006) FIXED POINTS OF COUNTABLY CONDENSING MAPPINGS AND ITS APPLICATION TO NONLINEAR EIGENVALUE PROBLEMS. Journal of the Korean Mathematical Society 43:1, pages 1-9.
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Z Liu, R.P Agarwal & S.M Kang. (2004) On solvability of functional equations and system of functional equations arising in dynamic programming. Journal of Mathematical Analysis and Applications 297:1, pages 111-130.
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Z. Liu & J.S. Ume. (2003) On Properties of Solutions for a Class of Functional Equations Arising in Dynamic Programming. Journal of Optimization Theory and Applications 117:3, pages 533-551.
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Zeqing Liu. (2001) Existence Theorems of Solutions for Certain Classes of Functional Equations Arising in Dynamic Programming. Journal of Mathematical Analysis and Applications 262:2, pages 529-553.
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Chang Shihsen & Guo Weiping. (1993) On the existence and uniqueness theorems of solutions for the systems of mixed monotone operator equations with applications. Applied Mathematics 8:1, pages 1-14.
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Shih-sen Chang & Yi-Hai Ma. (1991) Coupled fixed points for mixed monotone condensing operators and an existence theorem of the solutions for a class of functional equations arising in dynamic programming. Journal of Mathematical Analysis and Applications 160:2, pages 468-479.
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Zhang Shi-sheng. (1991) Some existence theorems of common and coincidence solutions for a class of systems of functional equations arising in dynamic programming. Applied Mathematics and Mechanics 12:1, pages 33-39.
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