Fixed point theorems via generalized $$\varvec{F}$$ F -contractions with applications to functional equations occurring in dynamic programming

Applications of Graph Kannan Mappings to the Damped Spring-Mass System and Deformation of an Elastic Beam

“…For a sequence { } ∈ if ( +1 ) for all ∈ N, then we say that { } is a -termwise connected (in short -) sequence. Singh et al in [21,22] proposed some notable real world problems from engineering science and invoked their results to find the solution of these problems. Recently in [5], the authors applied the connected graph theory in metric fixed point theory in a very interesting way and introduced graphical -metric space as a generalization of -metric space as follows.…”

New Existence of Fixed Point Results in Generalized Pseudodistance Functions with Its Application to Differential Equations

“…Thus, Piri and Kumam [7] generalized the result of Wordowski by using the conditions (F1), (F2 ) and (F3 ). Recently, Singk et al [11] removed the condition (F2 ) and it is called relaxed Fcontraction as follows.…”

“…In 2014, Pili and Kumam [7] revealed a large class of functions by changing condition (F3) to (F3 ) in the condition of F function. Afterwards, many authors used this mapping for studying the existences of fixed points and applied it to several problems [8][9][10][11]. Hence, by using the notion of F-contraction, we prove some new existence theorems of fixed points in generalized pseudodistances.…”

Some Common Fixed Point Theorems for Generalized F-Contraction Involving w-Distance with Some Applications to Differential Equations

“…Thus, Piri and Kumam [12] re-established the result of Wordowski using the conditions (F1), (F2 ) and (F3 ). Recently, Singk et al [13] drop-out the condition (F2 ) and named the contraction as the relaxed F-contraction as follows:…”

“…On the other hand, in 2012, Wardoski [10] introduced a new contraction called F-contraction and proved a fixed point point result, which generalizes Banach's contraction principal in many ways. Recently, Secelean [11], Piri and Kumam [12] and Singk et al [13] purified the result of Wardoski [10] by launching some weaker conditions on the mapping F (for more results on the F-contraction, see [14][15][16][17][18][19]).…”