Coincidence points of generalized multivalued \((f,L)\)-almost \(F\)-contraction with applications

Volume 8, Issue 6, pp 919--934 http://dx.doi.org/10.22436/jnsa.008.06.03

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Authors

Mujahid Abbas - Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa. Basit Ali - Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria 0002, South Africa. Salvador Romaguera - Instituto Universitario de Matematica Pura y Aplica, Universitat Politécnica de Valencia, Camí de Vera s/n, 46022 Valencia, Spain.

Abstract

Recently Abbas [M. Abbas, Coincidence points of multivalued \(f\)-almost nonexpansive mappings, Fixed Point Theory, 13 (1) (2012), 3-10] introduced the concept of \(f\)-almost contraction which generalizes the class of multivalued almost contraction mapping and obtained coincidence point results for this new class of mappings. We extend this notion to multivalued \(f\)-almost \(F\)-contraction mappings and prove the existence of coincidence points for such mappings. As a consequence, coincidence point results are obtained for generalized multivalued \(f\)-almost \(F\)-nonexpansive mappings which assume closed values only. Related common fixed point theorems are also proved. In the last section, applications of our results in dynamic programming and integral equations to show the existence and uniqueness of solutions are obtained. We present some remarks to show that our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.

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Keywords

• Coincidence point
• multivalued \(f\)-almost weak contraction
• star shaped sets
• integral equations
• dynamic programming.

MSC

•  47H04
•  47H10
•  54H25
•  60H25

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