الفهرس 
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Abstract
Fixed point theory becomes an important tool for solving various
problems in our everyday life. It is applied in chemistry, biology,
computer science, engineering, economics, game theory,mathematicaleconomics, differential equations and integral equations.
In 1912, Brouwer [24] proved that a continuous mapping on a
closed unit ball in Rn has a fixed point. Also, in 1930, Schauder
[71] states that a continuous mapping on a convex compact subspaceof a Banach space has a fixed point. On the other hand,
in 1922, Banach [18] introduced a notion called Banach’s contractionprinciple (abbrev. BCP). The (BCP) states that a contractionmapping on a complete metric space has a unique fixed point.However, various results improved the contraction mapping orthe complete space or both. There were more than one generalizedcontraction condition in [1, 3, 4, 5, 15, 25, 27, 32, 38, 39,42, 46, 51, 52, 62, 68] and others. For more comparisons amongseveral contractive conditions (see [47, 53, 66]).
As a multi-valued extension of (BCP), in 1969, Nadler [58]
introduced the notion of Nadler’s contraction principle (abbrev.
NCP). Actually, (NCP) may be an important extension of (BCP).
Some results of single-valued mappings extended into multi-valuedsettings such as [48, 49, 50, 56, 57, 76].
In this thesis, we prove some fixed points for single-valued,
multi-valued, hybrid, fuzzy and L-fuzzy mappings. Further, we
apply some of our results in various spaces. Finally, some of our
results extend, improve and generalize previous results in metric,
b-metric, fuzzy metric, intuitionistic fuzzy metric and L-fuzzy
metric spaces.
In Chapter 1, we give definitions of fixed points for singlevalued,
multi-valued, hybrid, fuzzy and L-fuzzy mappings. Further,
we list the concepts of fuzzy sets, fuzzy mappings, L-fuzzy
sets and L-fuzzy mappings. Also, we list the notions of b-metric,
ordered b-metric, fuzzy metric, intuitionistic fuzzy metric and L-fuzzymetric spaces. We write the basic definitions that will be
used in the sequent chapters.
In Chapter 2, we establish some common fixed point theorems
for fuzzy and crisp mappings under integral type of a contractive
condition in metric spaces. Also, we prove common fixed
point theorems for L-fuzzy mappings under implicit relation in
b-metric spaces. Finally, we prove some common fixed point theoremsfor L-fuzzy mappings in ordered b-metric spaces.
Some results of this chapter have been published in [10, 11,
14].
In Chapter 3, we introduce the concept of joint common limit
range property (JCLR-property) for single-valued and set-valued
maps in non-Archimedean fuzzy metric spaces. Further, we establishcommon fixed point theorems using implicit relation with
integral contractive condition. Several examples to illustrate the
significant of our results are given. Also, we prove existence of
common fixed point of L-fuzzy mappings on non-Archimedean orderedfuzzy metric spaces by using integral type and contractive
conditions. Finally, we state and prove common fixed point theoremsfor set-valued mappings in fuzzy metric spaces.
Some results of this chapter have been published in [21, 22].
In Chapter 4, we adopt the notion of JCLR-property for hybrid
pairs of L-fuzzy mappings in non-Archimedean modified intuitionisticfuzzy metric spaces. Also, we prove some common fixedpoints for L-fuzzy mappings in non-Archimedean modified intuitionisticfuzzy metric spaces. Our results generalize and improveseveral previous results [6, 12, 13, 26]. We support our results byintroducing illustrative examples.
Some results of this chapter have been published in [44].
In Chapter 5, we prove fixed points for hybrid pairs of L-fuzzy
and non self mappings in non-Archimedean L-fuzzy metric
spaces. These theorems extend, generalize and improve correspondingprevious results in metric, fuzzy metric, intuitionisticfuzzy metric and L-fuzzy metric spaces.
Some results of this chapter have been published in [8, 9].