and Applied Analysis 3 and satisfy the condition ∂ ∂θ ( arg f ( re )) Re { zh′ − zg ′ h g } > α 1.8 in D, where 0 ≤ α < 1. For two analytic functions f1 and f2, if f1 z ∞ ∑ j 1 ajz j , f2 z ∞ ∑ j 1 Ajz j , 1.9 then the convolution of f1 and f2 is defined by ( f1 ∗ f2 ) z f1 z ∗ f2 z ∞ ∑ j 1 ajAjz j . 1.10 By using the convolution, in 16 , Ali et al. introduced the class SH φ, σ, α of harmonic m...

Proposition 1. (Grunewald [5, Proposition B]) Let F be a free group of rank k ≥ 2, generated by {s1, . . . , sk}. Let r1, . . . , rm be words over {s1, . . . , sk} ±1 and R their normal closure 〈〈r1, . . . , rm〉〉F in F . Let H be the group with presentation 〈s1, . . . , sk | r1, . . . , rm〉 and φ the canonical epimorphism φ : F → H ∼= F/R. Let F be a free group of rank k generated by {t1, . . ....

Let (X,Y ) be random variables where X ∈ X is a vector of d features and Y ∈ {0, 1} represents a binary class label. A data set that contains independent observations {(xi, yi)} i=1 sampled from the joint distribution of (X,Y ) are often divided into training data {(xi, yi)}i=1 and test data {(xi, yi)} i=n+1. Based on training data, a classifier φ(·) is a mapping φ : X → {0, 1} that returns the...

Abstract. In this paper, we introduce contractive conditions of integral type in the setting of dislocated quasi b-metric spaces. Using contractive conditions of integral type, we have presented a fixed point theorem in the framework of dislocated quasi b-metric spaces. Our established result generalize and extend various fixed point theorems of the literature in the context of dislocated quasi...

The aim of this paper is to prove a common fixed point theorem for variants of weak compatible maps in a complex valued metric space. As a consequence, we extend and generalize the theorem of Branciari [3] for 2812 a pair of weakly compatible mappings satisfying a general contractive condition of integral type in complex valued metric space. At last, we prove two results by using E.A. property ...