No abstract

In this paper, a new class of noncommuting mappings as J H-operator pairs of type (R) are introduced and some examples are presented. Also, a common fixed point theorem for this kind of mappings is proved. Finally, as an application, the existence of a solution of nonlinear integral equations is proved. Keywords Common fixed point · J H-operator pair · J H-operator pair of type (R) · Nonlinear integral equation Mathematics Subject Classification (2010) 47H09

In this paper, some fixed-point theorems are established for strongly subadditive maps on CΩ,ϒ (where CΩ,ϒ denotes the space of ϒ-valued continuous functions on a compact Hausdorff space Ω and ϒ is a unital Banach algebra). Finally, the result is applied to prove the existence and uniqueness of a solution for a system of nonlinear integrodifferential equations.

In this paper, first some results of [5] are extended for subadditive separating maps between C(X, E) and C(Y, E), such that E is a unital Banach algebra. Then we give some conditions under which a strongly subadditive map has a unique fixed point. Finally as an application the existence and uniqueness of solution for a nonlinear integral equation is discussed.2010 Mathematics Subject Classification. 45G10, 37C25, 46J10. Key words and phrases. pointwise subadditive-strongly subadditive map-fixed point-integral equation.yousef estaremi

We initiate the concept of $C^{*}$-algebra-valued $G_{b}$-metric spaces. We study some basic properties of such spaces and then prove some fixed point theorems for Banach and Kannan types via $\mathit{C_{*}}$-class functions. Also, some nontrivial examples are presented to ensure the effectiveness and applicability of the obtained results.