Coincidence points of generalized multivalued \((f,L)\)-almost \(F\)-contraction with applications
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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.
Share and Cite
ISRP Style
Mujahid Abbas, Basit Ali, Salvador Romaguera, Coincidence points of generalized multivalued \((f,L)\)-almost \(F\)-contraction with applications, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 6, 919--934
AMA Style
Abbas Mujahid, Ali Basit, Romaguera Salvador, Coincidence points of generalized multivalued \((f,L)\)-almost \(F\)-contraction with applications. J. Nonlinear Sci. Appl. (2015); 8(6):919--934
Chicago/Turabian Style
Abbas, Mujahid, Ali, Basit, Romaguera, Salvador. "Coincidence points of generalized multivalued \((f,L)\)-almost \(F\)-contraction with applications." Journal of Nonlinear Sciences and Applications, 8, no. 6 (2015): 919--934
Keywords
- Coincidence point
- multivalued \(f\)-almost weak contraction
- star shaped sets
- integral equations
- dynamic programming.
MSC
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