Coincidence and fixed point theorems of generalized weakly contractive mappings in modular-like spaces

Subject Areas : Analyze

Fatemeh  Lael ¹ (Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran.)

Received: 2021-03-24 Accepted : 2022-05-06 Published : 2022-12-22

Keywords: فضای شبه‌مدولار, نگاشت‌های انقباضی به طور ضعیف تعمیم یافته, نقطه ثابت مشترک,

Abstract :

AbstractAlthough fixed point theorems in modular spaces have remarkably applied to a wide variety of mathematical problems, these theorems strongly depend on some assumptions which often do not hold in practice or can lead to their reformulations as particular problems in normed vector spaces. A recent trend of research has been dedicated to studying the fundamentals of fixed point theorems and relaxing their assumptions with the ambition of pushing the boundaries of fixed point theory in modular spaces further. The convexity is an assumption which lead to converting of modular space to the normed space so relaxing this assumption lead to stronger theorems. But as we know much theorems are proved on convex modular spaces.In this paper, we introduce the modular-like definition which is a generalization of modular space. And common fixed point of generalized weakly contraction mappings are proved. We focus on convexity and boundedness of modular-like in fixed point results taken from the literature for generalized weakly contractive mappings. So our results, generalized fixed point theorems in many acpects. Afterwards we present examples and an application to a particular form of integral inclusions to support our main results.

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