scholarly journals Fixed point theorems for nonlinear contractions with applications to iterated function systems

2018 ◽  
Vol 19 (1) ◽  
pp. 163
Author(s):  
Rajendra Pant
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Iterated Function Systems ◽  
Nonlinear Contraction ◽  
Iterated Function ◽  
New Type ◽  
Nonlinear Contractions

We introduce a new type of nonlinear contraction and present some fixed point results without using continuity or semi-continuity. Our result complement, extend and generalize a number of fixed point theorems including the the well-known Boyd and Wong theorem [On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969)]. Also we discuss an  application to  iterated function systems.

NONLINEAR RECURRENT HIDDEN VARIABLE FRACTAL INTERPOLATION CURVES WITH FUNCTION VERTICAL SCALING FACTORS

Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050096
Author(s):  
JINMYONG KIM ◽  
HAKMYONG MUN
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Iterated Function Systems ◽  
Vertical Scaling ◽  
Fractal Interpolation ◽  
Scaling Factors ◽  
Hidden Variable ◽  
Iterated Function

In this paper, we present a construction of new nonlinear recurrent hidden variable fractal interpolation curves. In order to get new fractal curves, we use Rakotch’s fixed point theorem. We construct recurrent hidden variable iterated function systems with function vertical scaling factors to generate more flexible fractal interpolation curves. We also give an illustrative example to demonstrate the effectiveness of our results.

scholarly journals A Solution for Volterra Fractional Integral Equations by Hybrid Contractions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 694 ◽  
Author(s):  
Alqahtani ◽  
Aydi ◽  
Karapınar ◽  
Rakočević
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fractional Integral ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Type ◽  
Linear Type ◽  
Linear And Nonlinear ◽  
Nonlinear Contractions ◽  
Type Contraction

In this manuscript, we propose a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces. Besides this main goal, we also aim to combine and merge several existing fixed point theorems that were formulated by linear and nonlinear contractions.

scholarly journals Tripled Fixed Points of Multivalued Nonlinear Contraction Mappings in Partially Ordered Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Mujahid Abbas ◽  
Hassen Aydi ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Contraction Mappings ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Contraction

Berinde and Borcut (2011), introduced the concept of tripled fixed point for single mappings in partially ordered metric spaces. Samet and Vetro (2011) established some coupled fixed point theorems for multivalued nonlinear contraction mappings in partially ordered metric spaces. In this paper, we obtain existence of tripled fixed point of multivalued nonlinear contraction mappings in the framework of partially ordered metric spaces. Also, we give an example.

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