[PDF] Top 20 Fixed Point Theorems for Nonlinear Operators with and without Monotonicity in Partially Ordered Banach Spaces

... about fixed points of nonlinear operators in partially ordered Banach spaces; see, for example, 1 and the proof of the following ... See full document

... fixed point theory, initiated by Ran and Reurings [] and continued by Nieto and Rodriguez-López [, ], is to consider a partial order on the ambi- ent metric space (X, d) and to transfer a part of the contractive ... See full document

... fixed point is introduced by Bhaskar and Lakshmikantham ...in partially ordered ...fixed point theory, we refer the readers to ...in partially ordered spaces (see, for ... See full document

... “Fixed point theorems for weakly contractive mappings in partially ordered sets,” Nonlinear ...“Fixed point theorems on ordered metric spaces ... See full document

... the Banach Contraction Principle has been generalized in various ...Hilbert spaces and proved the corresponding fixed point ...various fixed point and common fixed ... See full document

... the partially ordered Menger probabilistic metric spaces and establish some fixed-point theorems for mono- tone ...fixed point for a class of monotony ...fixed-point ... See full document

... () it extends Guo and Lakshmikantham’s coupled case, Berinde’s tripled case, Karapınar and Luong’s quadrupled case and Berzig and Samet’s multidimensional case. As we can easily see, the main result in [] (that the ... See full document

... Stefan Banach established a remarkable fixed point the- orem, the famous contraction principle, which is one of the most important results of ...fixed point result in different areas of mathemat- ics ... See full document

... fixed point theory for monotone operators in ordered Banach spaces has been inves- tigated extensively in the past  years ...fixed point theorems have been proved under ... See full document

... tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtained its ...monotone operators with ...tripled fixed point ... See full document

... monotone operators were introduced by Guo and Lakshmikantham in 1 in ...of operators in Banach spaces and obtained a lot of interesting and important ...in nonlinear differential and ... See full document

... coupled fixed point theorems and applied these to study the existence and uniqueness of solution for periodic boundary value ...coupled fixed point theorems for nonlinear ... See full document

... Later on, Lakshmikantham and Ciríc [8] proved coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete metric spaces..[r] ... See full document

... Fixed point results in partially ordered metric spaces play a major role in proving the existence and uniqueness of solutions for some differential and integral ...such theorems ... See full document

... In this case, 0, 0 and 1, 1 are both coupled fixed points of F and hence the coupled fixed point of F is not unique. This shows that the condition k < 1 in corollary 2.12 and hence k l < 1 in ... See full document

... coupled fixed point, and proved some coupled fixed point theorems for single valued mixed monotone ...coupled fixed point theorems in partially ... See full document

... metric spaces by replacing the set of real numbers with an ordered Banach space, for more details; see [4] and the references ...many fixed point results concerning self mappings in ... See full document

... coupled fixed point in partially ordered metric spaces,also discussed some problems of the uniqueness of a coupled fixed point and applied their results to the problems of ... See full document

... an ordered Banach space E: d : X × X → E. Such metric spaces are called cone metric spaces in short ...the fixed point theorems of Maia ...the fixed point ... See full document

... of fixed point results in PM-spaces is one of the most active research areas in fixed point ...a fixed point and common fixed point in PM-spaces, one ... See full document