Abstract
We generalize the notion of best proximity points in the context of modular function spaces. We have found sufficient conditions for the existence and uniqueness of best proximity points for cyclic maps in modular function spaces. We present an application of the main result for cyclic integral operators in Orlicz function spaces, endowed with an Orlicz function modular.
Highlights
A fundamental result in fixed point theory is the Banach contraction principle in Banach spaces or in complete metric spaces
Fixed point theory is an important tool for solving equations T x = x for mapping T defined on subsets of metric or normed spaces
Besides the idea of defining a norm and considering a Banach space, another direction of generalization of the Banach contraction principle is based on considering an abstractly given functional defined on a linear space, which controls the growth of the members of the space
Summary
A fundamental result in fixed point theory is the Banach contraction principle in Banach spaces or in complete metric spaces. Besides the idea of defining a norm and considering a Banach space, another direction of generalization of the Banach contraction principle is based on considering an abstractly given functional defined on a linear space, which controls the growth of the members of the space. This functional is usually called modular and defines a modular space. We have tried to generalize the idea of best proximity points in modular function spaces and to present an application for integral operators in Orlicz function spaces, endowed with an Orlicz function modular
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
