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Since shape-preserving approximation has many applications in computer-based geometric design, image processing, geodesy, chemistry, and robotics, we aim to implement divided difference methods to study the shape-preserving properties of a class of blending-type operators, which are constructed via certain shape parameters and represented in terms of divided differences. Considering this new representation, we establish the shape-preserving properties of operators, such as linearity, positivity, end-point interpolation and specifically monotonicity and convexity-preserving properties in connection with a function on the interval\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varvec{\\left[ 0,1\\right] }$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mfenced>\n                              <mml:mn>0<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:mfenced>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . Our theoretical, computational, and numerical results reveal that while operators preserve monotonicity entirely on the interval\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varvec{\\left[ 0,1\\right] }$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mfenced>\n                              <mml:mn>0<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:mfenced>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    for the defined intervals of shape parameters, they are unable to preserve the convexity of functions for some values of a shape parameter if the function has a monotonic behavior. Therefore, we give a modified convexity preservation result for the operators by imposing auxiliary assumptions on a function on the interval\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varvec{\\left[ 0,1\\right] }$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mfenced>\n                              <mml:mn>0<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:mfenced>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    . We conclude our analysis by providing a comparison of the convexity preservation abilities of operators equipped with the shape parameter\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\varvec{\\lambda }$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mi>\u03bb<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    .\n                  <\/jats:p>","DOI":"10.1007\/s11075-025-02134-5","type":"journal-article","created":{"date-parts":[[2025,6,29]],"date-time":"2025-06-29T19:55:31Z","timestamp":1751226931000},"page":"365-408","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Implementation of divided differences to shape preservation"],"prefix":"10.1007","volume":"102","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9012-4386","authenticated-orcid":false,"given":"Nezihe","family":"Turhan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,30]]},"reference":[{"key":"2134_CR1","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1017\/S026646660420305X","volume":"20","author":"A Sancetta","year":"2004","unstructured":"Sancetta, A., Satchell, S.: The bernstein copula and its applications to modeling and approximations of multivariate distributions. 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