Complex-valued double controlled metric like spaces with applications to fixed point theorems and Fredholm type integral equations

Abstract

<abstract><p>In this paper we introduce the concept of complex-valued double controlled metric like spaces. These new results generalize and extend the corresponding results about complex-valued double controlled metric type spaces. We prove some complex-valued fixed point theorems in this new complex-valued metric like spaces and, as application, we give an existence and uniqueness of the solution of a Fredholm type integral equation result. Moreover, some examples are also presented in favor of our given results.</p></abstract>

On Relational Weak Fℜm,η-Contractive Mappings and Their Applications

“…The classical Banach contraction theorem [1] is an important and fruitful tool in nonlinear analysis. In the past few decades, many authors have extended and generalized the Banach contraction mapping principle in several ways (see [2][3][4][5][6][7][8][9][10][11][12]). On the other hand, several authors, such as Boyd and Wong [13], Browder [14], Wardowski [15], Jleli and Samet [16], and many other researchers have extended the Banach contraction principle by employing different types of control functions (see [17][18][19][20][21] and the references therein).…”

Well-Posedness Scheme for Coupled Fixed-Point Problems Using Generalized Contractions

“…Researchers have been attempting to expand this idea by either embellishing the contraction condition or altering the properties of metric space in numerous contexts. Interested readers are encouraged to look at some recent extensions of BCP for finding fixed points and coupled fixed points in work by [2][3][4][5][6][7][8][9][10][11][12][13][14].…”