26 Results Found

In this work, we study some new applications of symmetric quantum calculus in the field of Geometric Function Theory. We use the cardioid domain and the symmetric quantum difference operator to generate new classes of multivalent q-starlike and q-con...

This paper introduces a new class of harmonic functions defined through a generalized symmetric q-differential that acts on both the analytic and co-analytic parts of the function. By combining concepts from symmetric q-calculus and geometric functio...

This paper presents a novel symmetric q-analogue differential operator designed for meromorphic multivalent functions analytic in the punctured open unit disk. Employing this operator, a new family of meromorphic multivalent functions is proposed and...

The main focus of this paper is to develop certain types of fundamental theorems using q, $q(\alpha )$, and h difference operators. For several higher order difference equations, we get two forms of solutions: one is closed form and another is summatio...

Our goal in this article is to use ideas from symmetric q-calculus operator theory in the study of meromorphic functions on the punctured unit disc and to propose a novel symmetric q-difference operator for these functions. A few additional classes o...

The main objective of this paper is to study a new family of analytic functions that are q-starlike with respect to m-symmetrical points and subordinate to the q-Janowski function. We investigate inclusion results, sufficient conditions, coefficients...

This paper introduces and studies a new class of analytic p-valent functions in the open symmetric unit disc involving the Sălăgean-type q-difference operator. Furthermore, we present several interesting subordination results, coefficient i...

Recently, the properties of analytic functions have been mainly discussed by means of a fuzzy subset and a q-difference operator. We define certain new subclasses of analytic functions by using the fuzzy subordination to univalent functions whose ran...

We create two Sakaguchi-type function classes that are starlike and convex with respect to their symmetric points, including a q-difference operator, which may have symmetric or assymetric properties, in the open unit disc. We first obtain sufficient...

In this study, we applied the ideas of subordination and the symmetric q-difference operator and then defined the novel class of bi-univalent functions of complex order $\gamma$. We used the Faber polynomial expansion method to determine the upper bou...

The goal of the present investigation is to introduce a new class of analytic functions ($K_{t,q}$), defined in the open unit disk, by means of the q-difference operator, which may have symmetric or assymetric properties, and to establish the relationship...

In this paper, we make use of the Riemann–Liouville fractional q-integral operator to discuss the class $S_{q,\delta }^{*}\left(\alpha \right)$ of univalent functions for $\delta >0,\alpha \in \mathbb{C}-\left\{0\right\}$, and $0<\left|q\right|<1$. Then, we develop convolution resul...

In this paper, we develop theorems on finite and infinite summation formulas by utilizing the $\mathfrak{q}$ and $(\mathfrak{q},\mathfrak{h})$ anti-difference operators, and also we extend these core theorems to ${\mathfrak{q}}_{\left(\alpha \right)}$ and ${(\mathfrak{q},\mathfrak{h})}_{\alpha }$ difference operators. Several integer order the...

In respect to the multi-attribute group decision making (MAGDM) problems in which the evaluated value of each attribute is in the form of q-rung orthopair fuzzy numbers (q-ROFNs), a new approach of MAGDM is developed. Firstly, a new aggregation opera...

In this article, we propose a different generalization of $(p,q)$ -BBH operators and carry statistical approximation properties of the introduced operators towards a function which has to be approximated where $(p,q)$ -integers cont...

The existence of solutions of nonlocal fractional symmetric Hahn integrodifference boundary value problem is studied. We propose a problem of five fractional symmetric Hahn difference operators and three fractional symmetric Hahn integrals of differe...

The research described in this paper follows the hypothesis that the monomiality principle leads to novel results that are consistent with past knowledge. Thus, in line with prior facts, our aim is to introduce the ${\Delta }_h$ multi-variate Hermite poly...

By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic...

This study follows the line of research that by employing the monomiality principle, new outcomes are produced. Thus, in line with prior facts, our aim is to introduce the ${\mathrm{\Delta }}_h$ multi-variate Hermite Appell polynomials ${}_{{\mathrm{\Delta }}_h}{}_{\mathfrak{H}}{\mathfrak{A}}_m^{\left[r\right]}(q_1,q_2,\cdots$...

The principal motivation of this paper is to establish a new integral equality related to k-Riemann Liouville fractional operator. Employing this equality, we present several new inequalities for twice differentiable convex functions that are associa...

In this paper, we introduce a comprehensive and expanded framework for generalized calculus and generalized polynomials in discrete calculus. Our focus is on $(q;h)$-time scales. Our proposed approach encompasses both difference and quantum problems, m...

As a typical model of three-way decisions (3WD), decision-theoretic rough sets (DTRS), have gained attention from scholars in decision-making problems. The q-rung orthopair fuzzy 2-tuple linguistic variable (QROF2-TLV) is a mixture of two different n...

As an attractive generalization of the intuitionistic fuzzy set (IFS), q-rung orthopair fuzzy set (q-ROFS) provides the decision makers (DMs) with a wide window for preference elicitation. Previous studies on q-ROFS indicate that there is an urge for...

The calculus in the absence of limits is known as quantum calculus. With a difference operator, it substitutes the classical derivative, which permits dealing with sets of functions that are non-differentiations. The theory of integral inequality in...

A paradigm for high-quality factor $(Q$) with a substantial fulfillment for appraising sensing ability and performance has been investigated. Through constructing a 1D (one-dimensional) topological photonic crystal (PhC) mirror heterostructure, which i...

The material in the mold of the injection-molding machine releases significant latent heat of solidification during the cooling process. The efficient recovery and utilization of this waste heat is crucial for improving energy efficiency. A novel int...