The purpose of this work is to present some local and global fixed point results for singlevalued and multivalued generalized contractions on spaces endowed with vector-valued metrics. The results are extensions of some theorems given by Perov 1964, Bucur et al. 2009, M. Berinde and V. Berinde 2007, O'Regan et al. 2007 , and so forth.

In this paper we extend some results of V. Berinde, Şt. Măruşter and I.A. Rus (Saturated contraction principles for nonself operators, generalizations and applications, Filomat, 31:11(2017), 3391-3406), which were given in metric spaces, to Kasahara spaces. Some research directions are also presented.

"In this paper we give conditions in which the integral equation $$x(t)=\displaystyle\int_a^c K(t,s,x(s))ds+\int_a^t H(t,s,x(s))ds+g(t),\ t\in [a,b],$$ where $a<c<b$, $K\in C([a,b]\times [a,c]\times \mathbb{B},\mathbb{B})$, $H\in C([a,b]\times [a,b]\times \mathbb{B},\mathbb{B})$, $g\in C([a,b],\mathbb{B})$, with $\mathbb{B}$ a (real or complex) Banach space, has a unique solution in $C([a,b],\mathbb{B})$. An iterative algorithm for this equation is also given."

The aim of this paper is to present existence and uniqueness results for the solution of a general system of Fredholm integral equations by applying the vectorial form of Maia's fixed‐point theorem. A Gronwall‐type lemma and comparison theorems are also obtained.

The aim of this paper is to present a fixed point theory for S-contractions in generalized Kasahara spaces (X, →, d), where d : X × X → s(R + ) is not necessarily an s(R + )-metric.