In this paper, we prove some new fixed point theorems involving set-valued F-contractions in the setting of quasi-ordered metric spaces. Our results are significant since present Banach contraction principle a different manner from that which is known literature. Some examples and an application to existence solution Volterra-type integral equation given support obtained

In this paper, we discuss and extend some recent common fixed point results established by using $varphi-$weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a $C-$class function. Using $C-$class functions, we generalize some known fixed point results. This type of functions is a very important class of ...

This paper is devoted to the study of establishing sufficient conditions for existence and uniqueness of positive solution to a class of non-linear problems of fractional differential equations. The boundary conditions involved Riemann-Liouville fractional order derivative and integral. Further, the non-linear function $f$ contain fractional order derivative which produce extra complexity. Than...

In this paper, we introduce a new contraction-type mapping and provide fixed-point theorem which generalizes improves some existing results in the literature. Thus, prove that Boyd Wong (1969) and, more recently, due to Wardowski (2012), Turinici Piri Kumam (2016), Secelean Proinov (2020), others are consequences of our main result. An application integral equations illustrative examples indica...

We use the contraction mapping theorem to present existence and uniqueness of solutions in a short time system non-linear Volterra integral equations certain type direct-sum H[a; b] Hilbert space V[a; b]. extend local global proposed problem. Because kernel function is transcendental on interval [a; b], results are novel very important numerical approximation.

In this article, we introduce a new concept of admissible contraction and prove fixed point theorems which generalize Banach principle in different way more than the known results from literature. The article includes an example shows validity our results, additionally obtain solution integral equation by mapping setting b-metric spaces.

in this paper, an attempt is made to present an extension of darbo's theorem, and its applicationto study the solvability of a functional integral equation of volterra type.