Common fixed point theorems for auxiliary functions with applications in fractional differential equation
نویسندگان
چکیده
Abstract In this work, we investigate h - ϕ contraction mappings with two metrics endowed a directed graph which involve auxiliary functions. The achievement allows us to obtain applications for the existence of solutions Caputo fractional boundary value problems integral condition type. addition, also give examples and numerical experiments supporting our main results.
منابع مشابه
Fixed Point Theorems via Auxiliary Functions
Fixed point theory is one of fundamental tools of nonlinear functional analysis. Since the fixed point theory has a wide application area in almost all quantitative sciences, many authors have been working on this field. One of the impressive initial results in this direction was given by Banach 1 , known as Banach Contraction Mapping Principle. It states that each contraction in a complete met...
متن کاملFixed point theorems for generalized concave operators and applications to fractional differential equation boundary value problems
In this paper, by introducing the concept of a generalized concave operator and the properties of cone and monotone iterative technique in ordered Banach spaces, some new existence and uniqueness theorems of fixed points for the operator under more extensive conditions are obtained. Finally, as applications, we apply the results obtained in this paper to study the existence and uniqueness of po...
متن کاملCoupled common fixed point theorems for $varphi$-contractions in probabilistic metric spaces and applications
In this paper, we give some new coupled common fixed point theorems for probabilistic $varphi$-contractions in Menger probabilistic metric spaces. As applications of the main results, we obtain some coupled common fixed point theorems in usual metric spaces and fuzzy metric spaces. The main results of this paper improvethe corresponding results given by some authors. Finally, we give one exa...
متن کاملCommon fixed point theorems for occasionally weakly compatible mappings in Menger spaces and applications
In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to ...
متن کاملFixed point theorems under weakly contractive conditions via auxiliary functions in ordered $G$-metric spaces
We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2021
ISSN: ['1687-1839', '1687-1847']
DOI: https://doi.org/10.1186/s13662-021-03660-x